NP evidences + hadronic uncertainties in b sll: The state-of-the-art

NP evidences + hadronic uncertainties in b sll: The state-of-the-art Joaquim Matias Universitat Autònoma de Barcelona Moriond EW In collaboration with: B. Capdevila, S. Descotes-Genon, L. Hofer and J. Virto Based on: CDVM 16 (JHEP 1610 (2016) 075) and CDHM 17 arxiv:1701.08672 (to appear in JHEP).

Present situation concerning evidences of NP in b sll

W b sµµ effective Hamiltonian l + l + l l O 7,7 c, t b s W B M B M l + l + l l O 7,7 O 9,10,9,10... b sγ( ) : H SM F =1 V tsv tb C i O i +... separate short and long distances (µ b = m b ) O 7 = O 9 = O 10 = e 16π 2 m b sσ µν (1 + γ 5 )F µν b [real or soft photon] e2 sγ 16π 2 µ (1 γ 5 )b lγ µ l [b sµµ via Z /hard γ... ] e2 sγ 16π 2 µ (1 γ 5 )b lγ µ γ 5 l [b sµµ via Z ] C SM 7 = 0.29, C SM 9 = 4.1, C SM 10 = 4.3 B M B M A= C i (short dist) Hadronic quantities (long dist) B O 9,10,9,10... l + l M 1 NP changes short-distance C i for SM or involve additional operators O i Chirally flipped (W W R ) O 7 sσ µν (1 γ 5 )F µν b (Pseudo)scalar (W H + ) Tensor operators (γ T ) 2 O S s(1 + γ 5 )b ll, O P O T sσ µν (1 γ 5 )b lσ µν l Using symmetries in E K and HQL: A i, V i, T i full-ff ξ, (SFF)

P 5 anomaly (Preludio) P 5 0.5 0.0 0.5 1.0 0 5 10 15 q GeV P 5 was proposed in DMRV, JHEP 1301(2013)048 P 5 = 2 Re(AL 0 AL AR 0 A AR 0 2 ( A 2 + A 2 ) = P 5 ) ( 1 + O(αs ξ ) + p.c. ). Optimized Obs.: Soft form factor (ξ ) cancellation at LO. 2013: 1fb 1 dataset LHCb found 3.7σ 2015: 3fb 1 dataset LHCb (in blue) found 3σ in 2 bins. Predictions (in red) from DHMV. Belle confirmed it in a bin [4,8] few months ago. Geometrical Interpretation: in absence of RHC, cosine of the relative angle between the perpendicular transversity vector n and the longitudinal n 0. High sensitivity to C 9 and smaller to C 10 : P 5 = 1 [ N Re (C9 eff + 2mˆ bc7 eff )(C9 eff + 2 ˆ m b ŝ Ceff 7 ) (C9+ eff + 2mˆ bc eff 7 )(C eff 9+ + 2 ˆ where C eff 9± = Ceff 9 ± C 10 ] 7 ) m b ŝ Ceff

P 5 anomaly (Preludio) Belle confirmed it in a bin [4,8] few months ago. P 5 1.5 1.0 0.5 0.0 0.5 1.0 Belle preliminary This Analysis LHCb 2013 LHCb 2015 SM from DHMV 1.5 0 5 10 15 20 q 2 (GeV 2 /c 4 ) High sensitivity to C 9 and lower to C 10 : P 5 = 1 [ N Re (C9 eff + 2mˆ bc7 eff )(C9 eff + 2 ˆ P 4 m b ŝ Ceff 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 Belle preliminary This Analysis LHCb 2013 LHCb 2015 SM from DHMV 0 5 10 15 20 q 2 (GeV 2 /c 4 ) 7 ) (C9+ eff + 2mˆ bc eff 7 )(C eff 9+ + 2 ˆ ] 7 ) m b ŝ Ceff where C eff 9± = Ceff 9 ± C 10 A possible interpretation: in absence of RHC, cosine of the relative angle between n = (A L, AR ) and the longitudinal n 0 = (A L 0, AR 0 ).

P 5 anomaly (Preludio) 1.5 1.0 0.5 Belle preliminary This Analysis LHCb 2013 LHCb 2015 SM from DHMV P 5 was proposed in DMRV, JHEP 1301(2013)048 P 5 = 2 Re(AL 0 AL AR 0 A AR 0 2 ( A 2 + A 2 ) = P 5 ) ( 1 + O(αs ξ ) + p.c. ). P 5 0.0 0.5 1.0 1.5 0 5 10 15 20 q 2 (GeV 2 /c 4 ) Optimized Obs.: Soft form factor (ξ ) cancellation at LO. 2013: 1fb 1 dataset LHCb found 3.7σ 2015: 3fb 1 dataset LHCb (in blue) found 3σ in 2 bins. Predictions (in red) from DHMV. Belle confirmed it in a bin [4,8] few months ago. Large-recoil for K : 4m 2 l q2 9 GeV 2 and low-recoil: 14 GeV 2 q 2 2 (m B m K ) 2. 1 Computed in i-qcdf + KMPW+ 4-types of correct. F full (q 2 ) = F soft (ξ, ξ ) + F αs (q 2 ) + F p.c. (q 2 ) type of correction Factorizable Non-Factorizable α s -QCDF F αs (q 2 ) power-corrections F p.c. (q 2 ) LCSR with single soft gluon contribution

More Anomalies in B K ll LCSR Lattice Data c 4 /GeV 2 ] -8 [10 5 4 3 2 + + B K µ + µ LHCb b c, t l + l s db/dq 2 1 0 0 5 10 15 20 q 2 [GeV 2 /c 4 ] B W M q 2 invariant mass of ll pair Br(B K µµ) too low compared to SM R K = Br(B K µµ) Br(B Kee) = 0.745 +0.090 [1,6] 0.074 ± 0.036 equals to 1 in SM (universality of lepton coupling), 2.6 σ dev NP coupling to µ and e 1

Other tensions beyond P 5 and R K Systematic low-recoil small tensions (EXP too low compared with SM in several BR µ also at large-recoil): b sµ + µ (low-recoil) bin SM EXP Pull 10 7 BR(B 0 K 0 µ + µ ) [15,19] 0.91 ± 0.12 0.67 ± 0.12 +1.4 10 7 BR(B 0 K 0 µ + µ ) [16,19] 1.66 ± 0.15 1.23 ± 0.20 +1.7 10 7 BR(B + K + µ + µ ) [15,19] 2.59 ± 0.25 1.60 ± 0.32 +2.5 10 7 BR(B s φµ + µ ) [15,18.8] 2.20 ± 0.17 1.62 ± 0.20 +2.2 After including the BSZ DA correction that affected the error of twist-4: 10 7 BR(B s φµ + µ ) SM EXP Pull [0.1,2] 1.56 ± 0.35 1.11 ± 0.16 +1.1 [2,5] 1.55 ± 0.33 0.77 ± 0.14 +2.2 [5,8] 1.89 ± 0.40 0.96 ± 0.15 +2.2 A precise measurement of F L (to near to 1) around [1-2.5] GeV 2 will impact P 2 will have a strong impact in the global analysis pull.

Global analysis of b sµµ anomalies [Descotes, Hofer, JM, Virto] 96 observables in total (LHCb for exclusive, no CP-violating obs) B K µµ (P 1,2, P 4,5,6,8, F L in 5 large-recoil bins + 1 low-recoil bin)+available electronic observables. B s φµµ (P 1, P 4,6, F L in 3 large-recoil bins + 1 low-recoil bin) B + K + µµ, B 0 K 0 ll (BR) (l = e, µ) B X s γ, B X s µµ, B s µµ (BR), B K γ (A I and S K γ) Various tools inclusive: OPE excl large-meson recoil: QCD fact, Soft-collinear effective theory excl low-meson recoil: Heavy quark eff th, Quark-hadron duality

Global analysis of b sµµ anomalies 96 observables in total (LHCb for exclusive, no CP-violating obs) [Descotes, Hofer, JM, Virto] B K µµ (P 1,2, P 4,5,6,8, F L in 5 large-recoil bins + 1 low-recoil bin)+available electronic observables. B s φµµ (P 1, P 4,6, F L in 3 large-recoil bins + 1 low-recoil bin) B + K + µµ, B 0 K 0 ll (BR) (l = e, µ) B X s γ, B X s µµ, B s µµ (BR), B K γ (A I and S K γ) Various tools inclusive: OPE excl large-meson recoil: QCD fact, Soft-collinear effective theory excl low-meson recoil: Heavy quark eff th, Quark-hadron duality Frequentist analysis C i (µ ref ) = Ci SM + Ci NP, with Ci NP assumed to be real (no CPV) Experimental correlation matrix provided Theoretical inputs (form factors... ) with correlation matrix computed treating all theo errors as Gaussian random variables Hypotheses NP in some C i only (1D, 2D, 6D) to be compared with SM

Updated result pre-r K and pre-q i Includes updated BR(B K µ + µ ) + corrected BSZ for B s φµ + µ. P µbelle 5 would add +0.1 to +0.3σ. A scenario with a large SM-pull big improvement over SM and better description of data. Coefficient Best fit 1σ Pull SM (σ) C7 NP 0.02 [ 0.04, 0.00] 1.1 C9 NP 1.05 [ 1.25, 0.85] 4.7 C10 NP 0.55 [0.34, 0.77] 2.8 C7 NP 0.02 [ 0.00, 0.04] 0.9 C9 NP 0.06 [ 0.18, 0.30] 0.3 C10 NP 0.03 [ 0.20, 0.14] 0.2 C9 NP = C10 NP 0.18 [ 0.36, 0.02] 0.9 C9 NP = C10 NP 0.59 [ 0.74, 0.44] 4.3 C9 NP = C NP 10 0.03 [ 0.08, 0.13] 0.2 C9 NP = C9 NP 1.00 [ 1.20, 0.78] 4.4 C9 NP = C10 NP = C9 NP = C NP 10 0.61 [ 0.45, 0.45] 4.3 Table: Best-fit p., conf. interv., pulls for the SM hypothesis (σ) for different 1D Global fit: Results All deviations add up constructively A NP contribution to C 9,µ =-1.1 with a pull-sm above 4.5σ alleviates all anomalies and tensions. NP contributions to the rest of Wilson coefficient are not (for the moment) yet significantly different from zero. See A. Crivellin s, Panico s,... talk for models.

Beyond 1D several favoured scenarios Allowing for more than one Wilson coefficient to vary different scenarios with pull-sm beyond 4σ pop-up: 3 Branching Ratios 3 Branching Ratios 3 Branching Ratios Angular Observables P i Angular Observables P i Angular Observables P i 2 All 2 All 2 All 1 1 1 NP C 10 0 NP C 9' 0 NP C 10 NP C10' 0 1 1 1 2 2 2 3 3 2 1 0 1 2 3 C 9 NP 3 3 2 1 0 1 2 3 C 9 NP 3 3 2 1 0 1 2 3 C NP NP 9 C 9' (C 9, C 10 ) (C 9, C 9 ) (C 9 = C 9 & C 10 = C 10 ) BR and angular observables both favour C NP 9 1 in all good scenarios....my personal understanding (see back-up) from the analysis of each anomaly/tension is that with more data/precision ALL Wilson coefficients will switch on (including small contrib. primes and radiatives) in delicated cancellations in each observable.

Results in agreement with different analyses, regions and channels 3 Branching Ratios 2 Angular Observables P i All 1 NP C 10 0 1 2 NP Re(C 10 ) 3 3 2 1 0 1 2 3 2 1 0-1 -2 C 9 NP [Descotes, Hofer, JM, Virto] -3-2 -1 0 1 2 Re(C NP 9 ) [Altmanshoffer, Straub] [Hurth, Mahmoudi, Neshatpour] Different observables (LHCb only or averages, P i or J i ) Different form factor inputs Different treatments of hadronic corrections Same pattern of NP scenarios favoured (here, C9 NP, CNP 10 ) But also consistency between low and large recoil and between different modes.

Intermezzo... O 7,7 There have been some attempts by a few groups to try to explain B a subset of Mthe previous anomalies using two arguments: huge factorizable power corrections l + l l + l O 7,7 O 9,10,9,10... B M B M or unknown charm contributions... l + l c c l + l O 9,10,9,10... O i B B M M we will show (using illustrative examples) in a pedagogical way where these attempts fail. [See 1701.08672 for all details.] We will first discuss the theoretical arguments to deconstruct these explanations and later see what type of experimental evidences will help in fully closing the discussion (with the help of Nature). 2

Intermezzo... O 7,7 There have been some attempts by a few groups to try to explain B a subset of Mthe previous anomalies using two arguments: huge factorizable power corrections l + l (easy to discard) l + l O 7,7 O 9,10,9,10... B M B M or unknown charm contributions... (more difficult to discard but also possible) l + l c c O 9,10,9,10... O i l + l B B M M we will show here (using illustrative examples) in a pedagogical way where these attempts fail. [See 1701.08672 for all details.] We will first discuss the theoretical arguments to deconstruct these explanations and later see what type of experimental evidences will help in fully closing the discussion (with the help of Nature). 2

Can factorizable power corrections be an acceptable explanation? NO. Two main reasons: F full (q 2 ) = F soft (ξ, ξ ) + F αs (q 2 ) + F Λ (q 2 ) F Λ = (a F + a F ) + (b F + b F )q 2 /m 2 B +... 1 Scheme dependence: choice of definition of SFF ξ, in terms of full-ff. ALERT: Observables are scheme independent only if all correlations (including correlations of a F...) are included. Not including the later ones [Jaeger et.al. and DHMV] F PC = F O(Λ/m B ) require careful scheme choice: risk to inflate artificially the error in observables. 2 Correlations among observables via (a F,...) power corrections. Require a global view. Two methods: Our I-QCDF using SFF+corrections+KMPW-FF [Descotes-Genon, Hofer, Matias, Virto] Full-FF + eom using BSZ-FF [Bharucha, Straub, Zwicky] radically different treatment of factorizable p.c. give SM-predictions for P 5 in very good agreement (1σ or smaller).

About size Compare the ratio A 1 /V (that controls P 5 ) computed using BSZ (including correlations) and computed with our approach for different size of power corrections. 0.9 0.9 0.8 0.8 A1 V 0.7 A1 V 0.7 5 10 20 0.6 0.6 0.5 0.5 0.4 0 2 4 6 8 0.4 0 2 4 6 8 Assigning a 5% error (we take 10%) to the power correction error reproduces the full error of the full-ff!!! Let s illustrate now points 1 and 2 with two examples.

Scheme-dependence (illustrative example-i) F PC = F O(Λ/m B ) F 10% 1 correlations from large-recoil sym. ξ,, F PC uncorr. F PC from fit to LCSR 2 correlations from large-recoil sym. ξ,, F PC uncorr. P 5 [4.0, 6.0] scheme 1 [CDHM] scheme 2 [JC] 1 0.72 ± 0.05 0.72 ± 0.12 2 0.72 ± 0.03 0.72 ± 0.03 3 0.72 ± 0.03 0.72 ± 0.03 full BSZ 0.72 ± 0.03 errors only from pc with BSZ form factors [Capdevila, Descotes, Hofer, JM] F PC from fit to LCSR 3 correlations from LCSR ξ,, F PC corr. [Bharucha, Straub, Zwicky] as example (correlation provided) scheme indep. restored if F PC from fit to LCSR, with expected magnitude sensitivity to scheme can be understood analytically no uncontrolled large power corrections for P 5

Correlations (illustrative example-ii) How much I need to inflate the errors from factorizable p.c. to get 1-σ agreement with data for P 5[4,6] and P 1[4,6] individually? One needs near 40% p.c. for P 5[4,6] and 0% for P 1[4,6]. This would be in direct conflict with the two existing LCSR computations: KMPW and BSZ. But including the strong correlation between p.c. of P 5[4,6] and P 1[4,6] [CDHM] more than 60% (> 80% in bin [6,8]) is required!!! P 5 = P 5 ( 1 + 2a V 2a T ξ 2a V + ξ C 9, C 9, + C 9, +... C7 eff(c 9, C 9, C10 2 ) m b m B (C 9, + C 9, )(C9, 2 + C2 10 ) q 2 P5' [4,6] 0.0-0.2-0.4-0.6 P 1 = 2a V + ξ (C eff 9 C 9, + C 2 10 ) C 2 9, + +... C2 10-0.8-1.0 The leading term in red in P 5 is missing in JC 14. -1.0-0.5 0.0 0.5 P 1 [4,6]

Can charm-loop contribution be the answer to the anomalies? Problem: Charm-loop yields q 2 and hadronic-dependent contribution with O 7,9 structures that may mimic New Physics. C9i eff (q 2 ) = C 9 SMpert + C9 NP + C c c 9i (q2 ). i =,, 0 How to disentangle? Is our long-dist c c estimate using KMPW as order of magnitude correct? 1 Fit to C NP 9 bin-by-bin of b sµµ data: NP is universal and q 2 independent. Hadronic effect associated to c c dynamics is (likely) q 2 dependent. 1.0 0.5 0.0 C 9 NP 0.5 1.0 1.5 2.0 Global Fit 0 5 10 15 20 q GeV NP [2,5] The excellent agreement of bins [2,5], [4,6], [5,8]: C9 = 1.6 ± 0.7, NP [4,6] NP [5,8] C9 = 1.3 ± 0.4, C9 = 1.3 ± 0.3 shows no indication of additional q 2 dependence.

[Ciuchini et al.] introduced a polynomial in each amplitudes and fitted the h (K ) i (i =,, 0 and K = 0, 1, 2): A 0 L,R = A0 L,R (Y (q2 )) + N ( q 2 h (0) 0 + q 2 1GeV 2 h(1) 0 + q 4 ) 1GeV 4 h(2) 0 THIS IS A FIT to LHCb data NOT A PREDICTION! 2 Unconstrained Fit finds constant contribution similar for all helicity-amplitudes. In full agreement with our global fit. Problem: They interpret this constant universal contribution as of unknown hadronic origin?? Interestingly: the same constant also explains R K ONLY if it is of NP origin and NOT if hadronic origin. Constrained Fit: Imposing SM+ C c c 9i (from KMPW) at q 2 < 1 GeV 2 is highly controversial: arbitrary choice that tilts the fit, inducing spurious large q 4 -dependence. fit to first bin that misses the lepton mass approximation by LHCb Imposing C9i c c fitted = C9i c c KMPW, is inconsistent since Im[C9i c c ] was not computed in KMPW!! In [1611.04338] same authors claim that absence of large-q 4 terms also leads to acceptable fit.

Notice that a NP contribution to C 7 and C 9 induces ALWAYS a small q 4 contribution because: C NP i FF(q 2 ) In [Ciuchini et al.] it is explicitly stated that q 4 can only come from hadronic effects... 3 We repeated the fit using Frequentist and KMPW-FF comparing fits with higher-order polynomials. Conclusion: data require constant and linear contributions in q 2, in agreement with KMPW. no improvement in the quality of the fit by adding large-q 4 terms (associated to h (2) λ ) or higher-orders. if C NP 9 = 1.1 is used the fit improves substantially (more than adding 12 indep. parameters). [Capdevila, Hofer, JM, S. Descotes; Hurth, Mahmoudi, Neshatpour]

4 LHCb also performed in [1612.06764] a measurement of phase difference between: Candidates / (22 MeV/c 2 ) 300 250 200 150 100 50 0 50 LHCb C eff 9 = C short distance 9 + Breit Wigner resonances (ω, ρ 0, φ,...) Focus on the channel B + K + µ + µ. FF from lattice and extrapolated on the whole q 2 range. Conclusion: The measured phases gives a tiny interference between short and long-distance far from their pole mass. No significant contribution of the tails of charmonia at low q 2. Result agrees with KMPW estimates. LHCb fits coupling, phases and C 9 and C 10. 3σ deviation w.r.t SM in C 9 C 10 plane. SM. If C 10 = C10 SM then C 9 < C9 SM in agreement with our fits. Same exercise for B K µµ? data total short-distance resonances interference background 1000 2000 3000 4000 m rec µ µ [MeV/c 2 ] Re(C 10 ) 0 2 4 LHCb 99.7% 95.5% 68.3% SM 6 0 2 4 6 Re(C 9 ) NP C 10 3 2 1 0 1 2 Branching Ratios Angular Observables P i 3 3 2 1 0 1 2 3 C 9 NP All

Is there also an alternative path to close the discussion? Exploring Lepton Flavour non-universality Observables sensitive to the difference between b sµµ and b see: 1 They cannot be explained by neither factorizable power corrections nor long-distance charm. 2 They share same explanation than P 5 anomaly, assuming NP in e-mode is suppressed (OK with fit).

Example-I: R K and R K Three main types: Ratios of Branching Ratios [Bobeth, Hiller et al. 07, 10]: R K = BR(B K µµ) BR(B Kee) R K = BR(B K µµ) BR(B K ee) R φ = BR(Bs φµµ) BR(B s φee) Difference of Optimized observables: Q i = P µ i P e i Inheritate the excellent properties of optimized observables Ratios of coefficients of angular distribution. B i = J µ with i=5,6s. i /J e All are useful to find deviations from SM with tiny uncertainty, but to disentangle different NP scenarios Q i and B i are key observables. For instance, C NP 9µ = 1.1, CNP 9e i 1 = 0 and CNP 9µ = CNP 10µ = 0.65,CNP 9,10e = 0 (Predictions for R K in [1701.08672]) RK 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0 1 2 3 4 5 6 7 1.1 1.0 0.9 0.8 0.7 0.6 RK q 2 (GeV 2 ) 0 5 10 15 0 q GeV

Example-II: Q i observables. Probing NP in C 9,10 with Q i SM predictions (grey boxes), NP: C9,µ NP = 1.11 (scenario1) & CNP 9,µ = CNP 10,µ = 0.65 (scenario 2) with δc i = C i,µ C i,e (and C i,e SM) Q 2 = P µ 2 Pe 2 Q 5 = P µ 5 P e 5 Q 4 = P µ 4 P e 4 Q 2, Q 4 & Q 5 show distinctive signatures for the two NP scenarios considered. Differences in the high-q 2 bins of the large recoil region of Q 2 & Q 5 are quite significant. Lack of difference between scenario 2 and SM same reason why P 5 in scenario 2 is worst than scenario 1. Q 4 at very low-q 2 (second bin) is very promising to disentangle scenario 1 from 2.

Example-II: Q i observables. Probing right-handed currents (RHC) with Q i SM predictions (grey boxes), NP: C9,µ NP = 1.11 & CNP 9,µ = CNP 10,µ = 0.65 & CNP 9,µ = C NP 9,µ = 1.18 & CNP 10,µ = C NP 10,µ = 0.38. with δc i = C i,µ C i,e (and C i,e SM) Q 1,4 provide excellent opportunities to probe RHC in C 9,µ & C 10,µ. Q 1 shows significant deviations in presence of RHC. If C 7 = 0 at LO C 7 δc 9 0 = 2 m bm B C 10,µ δc 10 + ReC 9,µδC 9 s LO IT HAS a zero (besides s = 0) if δc 9 0. Q 1 = P µ 1 Pe 1 Q 4 = P µ 4 P e 4 Q 4 also at low-q 2 exhibits deviations if C 9,10,µ 0 when accurate precision in measurements is achieved.

First hint from Belle? 1.5 1.0 0.5 SM from DHMV/LQCD All Modes Electron Modes Muon Modes 1.0 0.5 1.0 0.5 P 5 0.0 Q5 0.0 Q5 0.0 0.5 1.0-0.5-0.5 1.5 0 5 10 15 20 q 2 [GeV 2 /c 2 ] -1.0 0 5 10 15 q 2 (GeV 2 ) -1.0 0 2 4 6 8 q 2 (GeV 2 ) different systematics than LHCb (combination of channels). Belle has found for P 5 µ [4,8] a 2.6σ deviation while 1.3σ for P 5 e [4,8] Q 5 points in the same direction as C NP 9µ = 1.1 scenario (in red)ṁore data needed for confirmation...

Example-III: B 5 & B 6s Observables (unique properties) Idea: Combine J µ i & Ji e to build combinations sensitive to some C i, with controlled sensitivitiy to long-distance charm. Lepton mass differences generates a non-zero contribution mainly in the first bin. If on an event-by-event basis experimentalist can measure J µ i /βµ : 2 B 5 = Jµ 5 /β2 µ J5 e/β2 e 1 B 6s = Jµ 6s /β2 µ J6s e /β2 e 1 SM Predictions: B i = 0.00 ± 0.00. When ŝ 0, B 5 = B 6s = δc 10 /C 10 Sensitivity to δc 10! If β l removed same conclusion but a bit shifted. 1st Bins: Capacity to distinguish C9,µ NP = 1.11 from C9,µ NP = CNP 10,µ = 0.65. B 5 B 6s

Conclusions Global point of view: We have shown that the same NP solution C NP 9,µ = 1.1, CNP 9,e = 0 alleviates all tensions: P 5, R K, low-recoil, B s φµ + µ,...with a global pull-sm of 4.7σ SM alternative explanations are in trouble from a global point of view. an experimental update of B K µµ from LHCb is of utmost importance now. Local point of view (closing eyes to all deviations except P 5 ): - Factorizable p.c.: We have proven that an inappropriate scheme s choice if correlations among p.c. are not considered inflates artificially the errors. - Long-distance charm: Explicit computation by KMPW do not explain the anomaly and neither a bin-by-bin analysis nor a fit to h (i) λ does not find any indication for a large unaccounted q4 -dep. (h (2) λ 0). Different sets of ULFV observables comparing B K ee & B K µµ (totally free from any long distance charm in the SM): Q i Observables: Q i P l i C 9l linear Observables: B 5,6s, B 5,6s J 5,6s R K, R φ,... can have a deep impact on the global significance of the fit and help in disentangling scenarios. Exciting times from ULFV observables (R K, Q i,...) to come.

Back-UP slides

Criteria: An appropriate scheme is a scheme that naturally minimizes the sensitivity to power corrections in the relevant observables if you take a F uncorrelated. A simple numerical example: Evaluate P 5 at q2 = 6 GeV 2 and remember that JC and DHMV takes error of p.c. UNCORRELATED: P 5(6 GeV 2 ) = P 5 (6 GeV 2 ) ( 1 + 0.18 a A 1 + a V 2a T1 ξ 0.73 a ) A 1 a V +... ξ Focus on the leading term and check what happens under the two schemes: Scheme-I (our) define ξ = V a V = 0 then leading term has 0.73( a A1 )/ξ Scheme-II (JC) define ξ = T 1 a T1 = 0 then leading term has 0.73( a A1 a V )/ξ Being uncorrelated effectively Scheme-II induces a factor 2 larger error than Scheme-I. Already found numerically in 1407.8526.

Anyway there is a positive evolution of predictions in JC that has drastically decreased from 1412.3183: to very recent predictions in 1604.04042

Lepton Flavour Non-Universality 3 BR B KΜΜ BR B Kee within 1,6 2 1 All b sμμ and b see LFU A separated fit to C9µ NP and CNP 9e including B B Kee + large-recoil B K ee observables finds: NP C 9 e 0 1 2 3 3 2 1 0 1 2 3 NP C 9 Μ Preference for LFU violation with no-np in b see. Increase SM pull by +0.5σ (from 4.2σ to 4.7σ) Observables sensitive to the difference between b sµµ and b see processes open a new window of clean observables. 1 They cannot be explained by neither factorizable power corrections nor long-distance charm. 2 They share same explanation than the P 5 anomaly, assuming NP in electronic mode is suppressed.

Is the deviation isolated or is it coherent everywhere? Table non-updated Fit C NP 9 Bestfit 1σ Pull SM N dof All b sµµ 1.09 [ 1.29, 0.87] 4.5 95 All b sll, l = e, µ 1.11 [ 1.31, 0.90] 4.9 101 All b sµµ excl. [5,8] region 0.99 [ 1.23, 0.75] 3.8 77 and also excl. R K Only b sµµ BRs 1.58 [ 2.22, 1.07] 3.7 31 Only b sµµ P i s 1.01 [ 1.25, 0.73] 3.1 68 Only B K µµ 1.05 [ 1.27, 0.80] 3.7 61 Only B s φµµ 1.98 [ 2.84, 1.29] 3.5 24 Only b sµµ at large recoil 1.30 [ 1.57, 1.02] 4.0 78 Base analysis all b sµµ: +4.5σ Add: electronic mode (R K ): +0.4 to 0.5σ excl. region [5,8]: -0.6 to -0.7σ Only b sµµ at low recoil 0.93 [ 1.23, 0.61] 2.8 21 Only b sµµ within [1,6] 1.30 [ 1.66, 0.93] 3.4 43 Only BR(B K ll) [1,6], l = e, µ 1.55 [ 2.73, 0.81] 2.4 10

A glimpse into the future: Wilson coefficients versus Anomalies C NP 9 C NP 10 C 9 C 10 R K P 5 [4,6],[6,8] B Bs φµµ B Bs µµ low-recoil best-fit-point + [100%] X + [36%] X [32%] + [21%] X [36%] + [75%] [75%] X But also C NP 7, C 7,... Table: ( ) indicates that a shift in the Wilson coefficient with this sign moves the prediction in the right direction. C NP 9 < 0 is consistent with all anomalies. This is the reason why it gives a strong pull. C10 NP, C 9,10 fail in some anomaly. BUT C10 NP is the most promising coefficient after C 9, but not enough. C 9, C 10 seems quite inconsistent between the different anomalies and the global fit. Conspiracies among Wilson coefficients change the situation, i.e., C 10 C 10 > 0 is ok, both +.